Local Installation

An error connecting to your database is common, but it isn’t necessarily a problem with WordPress itself.

-First, double check your wp-config.php file settings for the database name, database username and database password. This is where most errors occur.

-Then check that you don’t need to change the database host from “localhost” to something else.

-Check you have actually created a database with the same database name as is in your wp-config.php file.

This topic also has already been raised many times on these forums. See:
http://wordpress.org/search/Error+establishing+a+database+connection?forums=1